All the Emperor's sons have been forged out of both physical matter and pure psychic force. In some, this manifests as incredible psychic talents, in others more esoteric gifts, but all have some things in common. You are to Astartes what Astartes are to children, standing head and shoulders over your fellows and obviously superior in every measurable way. You can hurl around Terminator armoured Astartes like they were children or punch straight through their plating, move far faster than even Astartes sight can follow, and even briefly lift a small Titan under your own power. A breathing apparatus is largely useless for Primarchs, for excepting a few chemical weapons and hellish worlds, a Primarch can breathe just fine in nearly any environment and even fight for hours without air amid the void of space. Not only that, you possess a fairly quick regeneration ability; you will heal from bruises in mere seconds and fully recover cuts down to the bone in minutes for a regular cut to hours for having the flesh entirely stripped off. But it is already extremely difficult to actually wound a Primarch, who is capable of surviving shots from tank cannons, bathing in molten rock, and being shot through the eye with sniper rounds. The average Primarch is also notably extremely resistant to psychic powers – capable of largely shrugging off all but attacks from extremely rare, extremely powerful psykers, though you may lower your resistance if you wish to be easier to affect with psychic powers such as healing and buffs from your allies.
Your mind is every bit as honed as your body. Your towering intellect would be considered genius among the greatest of men, though naturally inferior to the Emperor Himself. At the least, you have perfect eidetic memory (though there are ways to make you forget) and can memorise vast quantities of information far faster than any living human has or ever will. Furthermore, all Primarchs seem remarkably resistant to Chaos corruption and possession; short of directly clutching a Daemon weapon, being wounded by a specific weapon meant to corrupt you personally, or willingly letting the power of Chaos into you, you do not fear the gradual insanity and corruption into darkness lesser men might face. A Primarch naturally has the kind of towering willpower to resist Chaos in general, even the Ruinous Powers must put some serious effort and elaborate plans into luring one over to their side.
You are, even before any other purchases, a very strong psyker. However, your powers most likely manifest as latent abilities you have no particular influence over, and many
Primarchs showed an... aversion to psychic powers that further limited their ability to develop them. If you were to deliberately apply yourself, learn to unlock your psychic potential and learn to safely use it, you could easily become an Alpha psyker at the very least. This is your raw potential and barring any other purchases in jump will begin entirely latent and untapped by yourself though it remains entirely possible you can awaken your gifts and reclaim your birthright as a mighty psychic demigod. Constant exposure to the Warp or the gifts of the Dark Gods may even empower you further...
Every Primarch was a different, individually crafted work of art, yet some of them had traits that were obviously non-human in origin. At the base level, you may add any particular purely cosmetic trait you wish to add that is within vaguely plausible human limits (scaled up to Primarch size of course).